Question

How to construct P QRS, such that l(PQ) = 3.5 cm, l(QR) = 5.6 cm, l(RS) = 3.5 cm, m∠Q = 110°, m∠R = 70°.
If it is given that c P QRS is a parallelogram, which of the given information is unnecessary?

Answer 1

Hi ,


PQRS is a parallelogram .

Opposite sides are parallel and equal.

PQ = RS = 3.5 cm

QR = PS = 5.6 cm

Steps to construction :

1 ) Draw PQ = 3.5 line segment .

2 ) Draw a ray QX such that <PQX = 110° .

3 ) draw an arc with Center Q and radius

5.6 cm intersects QX at R .

4 ) Take P and R centers and 5.6cm and

3.5 as radii draw two arcs intersecting

each other at S .

5 ) join P and R to S

Required PQRS Parallelogram formed .

Here ,

m<R = 70° is unnecessary.

I hope this helps you.

: )

Answer 2

Hi,

Answer: Given details are of Parallelogram.

Solution:

Properties of Parallelogram:

opposite sides are equal and parallel. In PQRS PQ║RS and PS ║ QR

Sum of Adjacent angles are 180°. i.e. ∠Q +∠R = 180°

same as ∠Q +∠P = 180°

Or opposite angles are same. i.e. ∠Q = ∠S and ∠P = ∠R

steps of construction:

first draw line QR of 5.6 cm.

Draw an angle of 110° at Q and 70° at R.

Measure length 3.5 cm with compass and make an arc from R to line of 70° and same from point Q.

Mark the points as S and P respectively.

Join point PS.

for Diagram look attachment.

hope it helps you.